/*
 *   This program is free software: you can redistribute it and/or modify
 *   it under the terms of the GNU General Public License as published by
 *   the Free Software Foundation, either version 3 of the License, or
 *   (at your option) any later version.
 *
 *   This program is distributed in the hope that it will be useful,
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *   GNU General Public License for more details.
 *
 *   You should have received a copy of the GNU General Public License
 *   along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

/*
 *    PrincipalComponents.java
 *    Copyright (C) 2000-2012 University of Waikato, Hamilton, New Zealand
 *
 */

package weka.attributeSelection;

import java.util.ArrayList;
import java.util.Enumeration;
import java.util.Vector;

import no.uib.cipr.matrix.Matrices;
import no.uib.cipr.matrix.SymmDenseEVD;
import no.uib.cipr.matrix.UpperSymmDenseMatrix;
import weka.core.Attribute;
import weka.core.Capabilities;
import weka.core.Capabilities.Capability;
import weka.core.DenseInstance;
import weka.core.Instance;
import weka.core.Instances;
import weka.core.Option;
import weka.core.OptionHandler;
import weka.core.SparseInstance;
import weka.core.Utils;
import weka.filters.Filter;
import weka.filters.unsupervised.attribute.Center;
import weka.filters.unsupervised.attribute.NominalToBinary;
import weka.filters.unsupervised.attribute.Remove;
import weka.filters.unsupervised.attribute.ReplaceMissingValues;
import weka.filters.unsupervised.attribute.Standardize;

/**
 * <!-- globalinfo-start --> Performs a principal components analysis and
 * transformation of the data. Use in conjunction with a Ranker search.
 * Dimensionality reduction is accomplished by choosing enough eigenvectors to
 * account for some percentage of the variance in the original data---default
 * 0.95 (95%). Attribute noise can be filtered by transforming to the PC space,
 * eliminating some of the worst eigenvectors, and then transforming back to the
 * original space.
 * <p/>
 * <!-- globalinfo-end -->
 * 
 * <!-- options-start --> Valid options are:
 * <p/>
 * 
 * <pre>
 * -C
 *  Center (rather than standardize) the
 *  data and compute PCA using the covariance (rather
 *   than the correlation) matrix.
 * </pre>
 * 
 * <pre>
 * -R
 *  Retain enough PC attributes to account 
 *  for this proportion of variance in the original data.
 *  (default = 0.95)
 * </pre>
 * 
 * <pre>
 * -O
 *  Transform through the PC space and 
 *  back to the original space.
 * </pre>
 * 
 * <pre>
 * -A
 *  Maximum number of attributes to include in 
 *  transformed attribute names. (-1 = include all)
 * </pre>
 * 
 * <!-- options-end -->
 * 
 * @author Mark Hall (mhall@cs.waikato.ac.nz)
 * @author Gabi Schmidberger (gabi@cs.waikato.ac.nz)
 * @version $Revision$
 */
public class PrincipalComponents extends UnsupervisedAttributeEvaluator implements AttributeTransformer, OptionHandler {

    /** for serialization */
    private static final long serialVersionUID = -3675307197777734007L;

    /** The data to transform analyse/transform */
    private Instances m_trainInstances;

    /** Keep a copy for the class attribute (if set) */
    private Instances m_trainHeader;

    /** The header for the transformed data format */
    private Instances m_transformedFormat;

    /** The header for data transformed back to the original space */
    private Instances m_originalSpaceFormat;

    /** Data has a class set */
    private boolean m_hasClass;

    /** Class index */
    private int m_classIndex;

    /** Number of attributes */
    private int m_numAttribs;

    /** Number of instances */
    private int m_numInstances;

    /** Correlation/covariance matrix for the original data */
    private UpperSymmDenseMatrix m_correlation;

    private double[] m_means;
    private double[] m_stdDevs;

    /**
     * If true, center (rather than standardize) the data and compute PCA from
     * covariance (rather than correlation) matrix.
     */
    private boolean m_center = false;

    /**
     * Will hold the unordered linear transformations of the (normalized) original
     * data
     */
    private double[][] m_eigenvectors;

    /** Eigenvalues for the corresponding eigenvectors */
    private double[] m_eigenvalues = null;

    /** Sorted eigenvalues */
    private int[] m_sortedEigens;

    /** sum of the eigenvalues */
    private double m_sumOfEigenValues = 0.0;

    /** Filters for original data */
    private ReplaceMissingValues m_replaceMissingFilter;
    private NominalToBinary m_nominalToBinFilter;
    private Remove m_attributeFilter;
    private Center m_centerFilter;
    private Standardize m_standardizeFilter;

    /** The number of attributes in the pc transformed data */
    private int m_outputNumAtts = -1;

    /**
     * the amount of variance to cover in the original data when retaining the best
     * n PC's
     */
    private double m_coverVariance = 0.95;

    /**
     * transform the data through the pc space and back to the original space ?
     */
    private boolean m_transBackToOriginal = false;

    /** maximum number of attributes in the transformed attribute name */
    private int m_maxAttrsInName = 5;

    /**
     * holds the transposed eigenvectors for converting back to the original space
     */
    private double[][] m_eTranspose;

    /**
     * Returns a string describing this attribute transformer
     *
     * @return a description of the evaluator suitable for displaying in the
     *         explorer/experimenter gui
     */
    public String globalInfo() {
        return "Performs a principal components analysis and transformation of " + "the data. Use in conjunction with a Ranker search. Dimensionality " + "reduction is accomplished by choosing enough eigenvectors to " + "account for some percentage of the variance in the original data---" + "default 0.95 (95%). Attribute noise can be filtered by transforming " + "to the PC space, eliminating some of the worst eigenvectors, and " + "then transforming back to the original space.";
    }

    /**
     * Returns an enumeration describing the available options.
     * <p>
     *
     * @return an enumeration of all the available options.
     **/
    @Override
    public Enumeration<Option> listOptions() {
        Vector<Option> newVector = new Vector<Option>(4);

        newVector.addElement(new Option("\tCenter (rather than standardize) the" + "\n\tdata and compute PCA using the covariance (rather" + "\n\t than the correlation) matrix.", "C", 0, "-C"));

        newVector.addElement(new Option("\tRetain enough PC attributes to account " + "\n\tfor this proportion of variance in " + "the original data.\n" + "\t(default = 0.95)", "R", 1, "-R"));

        newVector.addElement(new Option("\tTransform through the PC space and " + "\n\tback to the original space.", "O", 0, "-O"));

        newVector.addElement(new Option("\tMaximum number of attributes to include in " + "\n\ttransformed attribute names. (-1 = include all)", "A", 1, "-A"));
        return newVector.elements();
    }

    /**
     * Parses a given list of options.
     * <p/>
     *
     * <!-- options-start --> Valid options are:
     * <p/>
     *
     * <pre>
     * -C
     *  Center (rather than standardize) the
     *  data and compute PCA using the covariance (rather
     *   than the correlation) matrix.
     * </pre>
     *
     * <pre>
     * -R
     *  Retain enough PC attributes to account
     *  for this proportion of variance in the original data.
     *  (default = 0.95)
     * </pre>
     *
     * <pre>
     * -O
     *  Transform through the PC space and
     *  back to the original space.
     * </pre>
     *
     * <pre>
     * -A
     *  Maximum number of attributes to include in
     *  transformed attribute names. (-1 = include all)
     * </pre>
     *
     * <!-- options-end -->
     *
     * @param options the list of options as an array of strings
     * @throws Exception if an option is not supported
     */
    @Override
    public void setOptions(String[] options) throws Exception {
        resetOptions();
        String optionString;

        optionString = Utils.getOption('R', options);
        if (optionString.length() != 0) {
            Double temp;
            temp = Double.valueOf(optionString);
            setVarianceCovered(temp.doubleValue());
        }
        optionString = Utils.getOption('A', options);
        if (optionString.length() != 0) {
            setMaximumAttributeNames(Integer.parseInt(optionString));
        }

        setTransformBackToOriginal(Utils.getFlag('O', options));
        setCenterData(Utils.getFlag('C', options));
    }

    /**
     * Reset to defaults
     */
    private void resetOptions() {
        m_coverVariance = 0.95;
        m_sumOfEigenValues = 0.0;
        m_transBackToOriginal = false;
    }

    /**
     * Returns the tip text for this property
     *
     * @return tip text for this property suitable for displaying in the
     *         explorer/experimenter gui
     */
    public String centerDataTipText() {
        return "Center (rather than standardize) the data. PCA will " + "be computed from the covariance (rather than correlation) " + "matrix";
    }

    /**
     * Set whether to center (rather than standardize) the data. If set to true then
     * PCA is computed from the covariance rather than correlation matrix.
     *
     * @param center true if the data is to be centered rather than standardized
     */
    public void setCenterData(boolean center) {
        m_center = center;
    }

    /**
     * Get whether to center (rather than standardize) the data. If true then PCA is
     * computed from the covariance rather than correlation matrix.
     * 
     * @return true if the data is to be centered rather than standardized.
     */
    public boolean getCenterData() {
        return m_center;
    }

    /**
     * Returns the tip text for this property
     *
     * @return tip text for this property suitable for displaying in the
     *         explorer/experimenter gui
     */
    public String varianceCoveredTipText() {
        return "Retain enough PC attributes to account for this proportion of " + "variance.";
    }

    /**
     * Sets the amount of variance to account for when retaining principal
     * components
     *
     * @param vc the proportion of total variance to account for
     */
    public void setVarianceCovered(double vc) {
        m_coverVariance = vc;
    }

    /**
     * Gets the proportion of total variance to account for when retaining principal
     * components
     * 
     * @return the proportion of variance to account for
     */
    public double getVarianceCovered() {
        return m_coverVariance;
    }

    /**
     * Returns the tip text for this property
     *
     * @return tip text for this property suitable for displaying in the
     *         explorer/experimenter gui
     */
    public String maximumAttributeNamesTipText() {
        return "The maximum number of attributes to include in transformed attribute names.";
    }

    /**
     * Sets maximum number of attributes to include in transformed attribute names.
     *
     * @param m the maximum number of attributes
     */
    public void setMaximumAttributeNames(int m) {
        m_maxAttrsInName = m;
    }

    /**
     * Gets maximum number of attributes to include in transformed attribute names.
     * 
     * @return the maximum number of attributes
     */
    public int getMaximumAttributeNames() {
        return m_maxAttrsInName;
    }

    /**
     * Returns the tip text for this property
     *
     * @return tip text for this property suitable for displaying in the
     *         explorer/experimenter gui
     */
    public String transformBackToOriginalTipText() {
        return "Transform through the PC space and back to the original space. " + "If only the best n PCs are retained (by setting varianceCovered < 1) " + "then this option will give a dataset in the original space but with " + "less attribute noise.";
    }

    /**
     * Sets whether the data should be transformed back to the original space
     *
     * @param b true if the data should be transformed back to the original space
     */
    public void setTransformBackToOriginal(boolean b) {
        m_transBackToOriginal = b;
    }

    /**
     * Gets whether the data is to be transformed back to the original space.
     * 
     * @return true if the data is to be transformed back to the original space
     */
    public boolean getTransformBackToOriginal() {
        return m_transBackToOriginal;
    }

    /**
     * Gets the current settings of PrincipalComponents
     *
     * @return an array of strings suitable for passing to setOptions()
     */
    @Override
    public String[] getOptions() {

        Vector<String> options = new Vector<String>();

        if (getCenterData()) {
            options.add("-C");
        }

        options.add("-R");
        options.add("" + getVarianceCovered());

        options.add("-A");
        options.add("" + getMaximumAttributeNames());

        if (getTransformBackToOriginal()) {
            options.add("-O");
        }

        return options.toArray(new String[0]);
    }

    /**
     * Returns the capabilities of this evaluator.
     *
     * @return the capabilities of this evaluator
     * @see Capabilities
     */
    @Override
    public Capabilities getCapabilities() {
        Capabilities result = super.getCapabilities();
        result.disableAll();

        // attributes
        result.enable(Capability.NOMINAL_ATTRIBUTES);
        result.enable(Capability.NUMERIC_ATTRIBUTES);
        result.enable(Capability.DATE_ATTRIBUTES);
        result.enable(Capability.MISSING_VALUES);

        // class
        result.enable(Capability.NOMINAL_CLASS);
        result.enable(Capability.UNARY_CLASS);
        result.enable(Capability.NUMERIC_CLASS);
        result.enable(Capability.DATE_CLASS);
        result.enable(Capability.MISSING_CLASS_VALUES);
        result.enable(Capability.NO_CLASS);

        return result;
    }

    /**
     * Initializes principal components and performs the analysis
     *
     * @param data the instances to analyse/transform
     * @throws Exception if analysis fails
     */
    @Override
    public void buildEvaluator(Instances data) throws Exception {
        // can evaluator handle data?
        getCapabilities().testWithFail(data);

        buildAttributeConstructor(data);
    }

    private void buildAttributeConstructor(Instances data) throws Exception {
        m_eigenvalues = null;
        m_outputNumAtts = -1;
        m_attributeFilter = null;
        m_nominalToBinFilter = null;
        m_sumOfEigenValues = 0.0;
        m_trainInstances = new Instances(data);

        // make a copy of the training data so that we can get the class
        // column to append to the transformed data (if necessary)
        m_trainHeader = new Instances(m_trainInstances, 0);

        m_replaceMissingFilter = new ReplaceMissingValues();
        m_replaceMissingFilter.setInputFormat(m_trainInstances);
        m_trainInstances = Filter.useFilter(m_trainInstances, m_replaceMissingFilter);

        /*
         * if (m_normalize) { m_normalizeFilter = new Normalize();
         * m_normalizeFilter.setInputFormat(m_trainInstances); m_trainInstances =
         * Filter.useFilter(m_trainInstances, m_normalizeFilter); }
         */

        m_nominalToBinFilter = new NominalToBinary();
        m_nominalToBinFilter.setInputFormat(m_trainInstances);
        m_trainInstances = Filter.useFilter(m_trainInstances, m_nominalToBinFilter);

        // delete any attributes with only one distinct value or are all missing
        Vector<Integer> deleteCols = new Vector<Integer>();
        for (int i = 0; i < m_trainInstances.numAttributes(); i++) {
            if (m_trainInstances.numDistinctValues(i) <= 1) {
                deleteCols.addElement(new Integer(i));
            }
        }

        if (m_trainInstances.classIndex() >= 0) {
            // get rid of the class column
            m_hasClass = true;
            m_classIndex = m_trainInstances.classIndex();
            deleteCols.addElement(new Integer(m_classIndex));
        }

        // remove columns from the data if necessary
        if (deleteCols.size() > 0) {
            m_attributeFilter = new Remove();
            int[] todelete = new int[deleteCols.size()];
            for (int i = 0; i < deleteCols.size(); i++) {
                todelete[i] = (deleteCols.elementAt(i)).intValue();
            }
            m_attributeFilter.setAttributeIndicesArray(todelete);
            m_attributeFilter.setInvertSelection(false);
            m_attributeFilter.setInputFormat(m_trainInstances);
            m_trainInstances = Filter.useFilter(m_trainInstances, m_attributeFilter);
        }

        // can evaluator handle the processed data ? e.g., enough attributes?
        getCapabilities().testWithFail(m_trainInstances);

        m_numInstances = m_trainInstances.numInstances();
        m_numAttribs = m_trainInstances.numAttributes();

        fillCovariance();

        SymmDenseEVD evd = SymmDenseEVD.factorize(m_correlation);

        m_eigenvectors = Matrices.getArray(evd.getEigenvectors());
        m_eigenvalues = evd.getEigenvalues();

        /*
         * for (int i = 0; i < m_numAttribs; i++) { for (int j = 0; j < m_numAttribs;
         * j++) { System.err.println(v[i][j] + " "); } System.err.println(d[i]); }
         */

        // any eigenvalues less than 0 are not worth anything --- change to 0
        for (int i = 0; i < m_eigenvalues.length; i++) {
            if (m_eigenvalues[i] < 0) {
                m_eigenvalues[i] = 0.0;
            }
        }
        m_sortedEigens = Utils.sort(m_eigenvalues);
        m_sumOfEigenValues = Utils.sum(m_eigenvalues);

        m_transformedFormat = setOutputFormat();
        if (m_transBackToOriginal) {
            m_originalSpaceFormat = setOutputFormatOriginal();

            // new ordered eigenvector matrix
            int numVectors = (m_transformedFormat.classIndex() < 0) ? m_transformedFormat.numAttributes() : m_transformedFormat.numAttributes() - 1;

            double[][] orderedVectors = new double[m_eigenvectors.length][numVectors + 1];

            // try converting back to the original space
            for (int i = m_numAttribs - 1; i > (m_numAttribs - numVectors - 1); i--) {
                for (int j = 0; j < m_numAttribs; j++) {
                    orderedVectors[j][m_numAttribs - i] = m_eigenvectors[j][m_sortedEigens[i]];
                }
            }

            // transpose the matrix
            int nr = orderedVectors.length;
            int nc = orderedVectors[0].length;
            m_eTranspose = new double[nc][nr];
            for (int i = 0; i < nc; i++) {
                for (int j = 0; j < nr; j++) {
                    m_eTranspose[i][j] = orderedVectors[j][i];
                }
            }
        }
    }

    /**
     * Returns just the header for the transformed data (ie. an empty set of
     * instances. This is so that AttributeSelection can determine the structure of
     * the transformed data without actually having to get all the transformed data
     * through transformedData().
     *
     * @return the header of the transformed data.
     * @throws Exception if the header of the transformed data can't be determined.
     */
    @Override
    public Instances transformedHeader() throws Exception {
        if (m_eigenvalues == null) {
            throw new Exception("Principal components hasn't been built yet");
        }
        if (m_transBackToOriginal) {
            return m_originalSpaceFormat;
        } else {
            return m_transformedFormat;
        }
    }

    /**
     * Return the header of the training data after all filtering - i.e missing
     * values and nominal to binary.
     *
     * @return the header of the training data after all filtering.
     */
    public Instances getFilteredInputFormat() {
        return new Instances(m_trainInstances, 0);
    }

    /**
     * Return the correlation/covariance matrix
     *
     * @return the correlation or covariance matrix
     */
    public double[][] getCorrelationMatrix() {
        return Matrices.getArray(m_correlation);
    }

    /**
     * Return the unsorted eigenvectors
     *
     * @return the unsorted eigenvectors
     */
    public double[][] getUnsortedEigenVectors() {
        return m_eigenvectors;
    }

    /**
     * Return the eigenvalues corresponding to the eigenvectors
     *
     * @return the eigenvalues
     */
    public double[] getEigenValues() {
        return m_eigenvalues;
    }

    /**
     * Gets the transformed training data.
     *
     * @return the transformed training data
     * @throws Exception if transformed data can't be returned
     */
    @Override
    public Instances transformedData(Instances data) throws Exception {
        if (m_eigenvalues == null) {
            throw new Exception("Principal components hasn't been built yet");
        }

        Instances output = null;

        if (m_transBackToOriginal) {
            output = new Instances(m_originalSpaceFormat);
        } else {
            output = new Instances(m_transformedFormat);
        }
        for (int i = 0; i < data.numInstances(); i++) {
            Instance converted = convertInstance(data.instance(i));
            output.add(converted);
        }

        return output;
    }

    /**
     * Evaluates the merit of a transformed attribute. This is defined to be 1 minus
     * the cumulative variance explained. Merit can't be meaningfully evaluated if
     * the data is to be transformed back to the original space.
     *
     * @param att the attribute to be evaluated
     * @return the merit of a transformed attribute
     * @throws Exception if attribute can't be evaluated
     */
    @Override
    public double evaluateAttribute(int att) throws Exception {
        if (m_eigenvalues == null) {
            throw new Exception("Principal components hasn't been built yet!");
        }

        if (m_transBackToOriginal) {
            return 1.0; // can't evaluate back in the original space!
        }

        // return 1-cumulative variance explained for this transformed att
        double cumulative = 0.0;
        for (int i = m_numAttribs - 1; i >= m_numAttribs - att - 1; i--) {
            cumulative += m_eigenvalues[m_sortedEigens[i]];
        }

        return 1.0 - cumulative / m_sumOfEigenValues;
    }

    private void fillCovariance() throws Exception {
        // first store the means
        m_means = new double[m_trainInstances.numAttributes()];
        m_stdDevs = new double[m_trainInstances.numAttributes()];
        for (int i = 0; i < m_trainInstances.numAttributes(); i++) {
            m_means[i] = m_trainInstances.meanOrMode(i);
            m_stdDevs[i] = Math.sqrt(Utils.variance(m_trainInstances.attributeToDoubleArray(i)));
        }

        // just center the data or standardize it?
        if (m_center) {
            m_centerFilter = new Center();
            m_centerFilter.setInputFormat(m_trainInstances);
            m_trainInstances = Filter.useFilter(m_trainInstances, m_centerFilter);
        } else {
            m_standardizeFilter = new Standardize();
            m_standardizeFilter.setInputFormat(m_trainInstances);
            m_trainInstances = Filter.useFilter(m_trainInstances, m_standardizeFilter);
        }

        // now compute the covariance matrix
        m_correlation = new UpperSymmDenseMatrix(m_numAttribs);
        for (int i = 0; i < m_numAttribs; i++) {
            for (int j = i; j < m_numAttribs; j++) {

                double cov = 0;
                for (Instance inst : m_trainInstances) {
                    cov += inst.value(i) * inst.value(j);
                }

                cov /= m_trainInstances.numInstances() - 1;
                m_correlation.set(i, j, cov);
            }
        }
    }

    /**
     * Return a summary of the analysis
     *
     * @return a summary of the analysis.
     */
    private String principalComponentsSummary() {
        StringBuffer result = new StringBuffer();
        double cumulative = 0.0;
        Instances output = null;
        int numVectors = 0;

        try {
            output = setOutputFormat();
            numVectors = (output.classIndex() < 0) ? output.numAttributes() : output.numAttributes() - 1;
        } catch (Exception ex) {
        }
        // tomorrow
        String corrCov = (m_center) ? "Covariance " : "Correlation ";
        result.append(corrCov + "matrix\n" + matrixToString(Matrices.getArray(m_correlation)) + "\n\n");
        result.append("eigenvalue\tproportion\tcumulative\n");
        for (int i = m_numAttribs - 1; i > (m_numAttribs - numVectors - 1); i--) {
            cumulative += m_eigenvalues[m_sortedEigens[i]];
            result.append(Utils.doubleToString(m_eigenvalues[m_sortedEigens[i]], 9, 5) + "\t" + Utils.doubleToString((m_eigenvalues[m_sortedEigens[i]] / m_sumOfEigenValues), 9, 5) + "\t" + Utils.doubleToString((cumulative / m_sumOfEigenValues), 9, 5) + "\t" + output.attribute(m_numAttribs - i - 1).name() + "\n");
        }

        result.append("\nEigenvectors\n");
        for (int j = 1; j <= numVectors; j++) {
            result.append(" V" + j + '\t');
        }
        result.append("\n");
        for (int j = 0; j < m_numAttribs; j++) {

            for (int i = m_numAttribs - 1; i > (m_numAttribs - numVectors - 1); i--) {
                result.append(Utils.doubleToString(m_eigenvectors[j][m_sortedEigens[i]], 7, 4) + "\t");
            }
            result.append(m_trainInstances.attribute(j).name() + '\n');
        }

        if (m_transBackToOriginal) {
            result.append("\nPC space transformed back to original space.\n" + "(Note: can't evaluate attributes in the original " + "space)\n");
        }
        return result.toString();
    }

    /**
     * Returns a description of this attribute transformer
     *
     * @return a String describing this attribute transformer
     */
    @Override
    public String toString() {
        if (m_eigenvalues == null) {
            return "Principal components hasn't been built yet!";
        } else {
            return "\tPrincipal Components Attribute Transformer\n\n" + principalComponentsSummary();
        }
    }

    /**
     * Return a matrix as a String
     *
     * @param matrix that is decribed as a string
     * @return a String describing a matrix
     */
    public static String matrixToString(double[][] matrix) {
        StringBuffer result = new StringBuffer();
        int last = matrix.length - 1;

        for (int i = 0; i <= last; i++) {
            for (int j = 0; j <= last; j++) {
                result.append(Utils.doubleToString(matrix[i][j], 6, 2) + " ");
                if (j == last) {
                    result.append('\n');
                }
            }
        }
        return result.toString();
    }

    /**
     * Convert a pc transformed instance back to the original space
     *
     * @param inst the instance to convert
     * @return the processed instance
     * @throws Exception if something goes wrong
     */
    private Instance convertInstanceToOriginal(Instance inst) throws Exception {
        double[] newVals = null;

        if (m_hasClass) {
            newVals = new double[m_numAttribs + 1];
        } else {
            newVals = new double[m_numAttribs];
        }

        if (m_hasClass) {
            // class is always appended as the last attribute
            newVals[m_numAttribs] = inst.value(inst.numAttributes() - 1);
        }

        for (int i = 0; i < m_eTranspose[0].length; i++) {
            double tempval = 0.0;
            for (int j = 1; j < m_eTranspose.length; j++) {
                tempval += (m_eTranspose[j][i] * inst.value(j - 1));
            }
            newVals[i] = tempval;
            if (!m_center) {
                newVals[i] *= m_stdDevs[i];
            }
            newVals[i] += m_means[i];
        }

        if (inst instanceof SparseInstance) {
            return new SparseInstance(inst.weight(), newVals);
        } else {
            return new DenseInstance(inst.weight(), newVals);
        }
    }

    /**
     * Transform an instance in original (unormalized) format. Convert back to the
     * original space if requested.
     *
     * @param instance an instance in the original (unormalized) format
     * @return a transformed instance
     * @throws Exception if instance cant be transformed
     */
    @Override
    public Instance convertInstance(Instance instance) throws Exception {

        if (m_eigenvalues == null) {
            throw new Exception("convertInstance: Principal components not " + "built yet");
        }

        double[] newVals = new double[m_outputNumAtts];
        Instance tempInst = (Instance) instance.copy();
        if (!instance.dataset().equalHeaders(m_trainHeader)) {
            throw new Exception("Can't convert instance: header's don't match: " + "PrincipalComponents\n" + instance.dataset().equalHeadersMsg(m_trainHeader));
        }

        m_replaceMissingFilter.input(tempInst);
        m_replaceMissingFilter.batchFinished();
        tempInst = m_replaceMissingFilter.output();

        /*
         * if (m_normalize) { m_normalizeFilter.input(tempInst);
         * m_normalizeFilter.batchFinished(); tempInst = m_normalizeFilter.output(); }
         */

        m_nominalToBinFilter.input(tempInst);
        m_nominalToBinFilter.batchFinished();
        tempInst = m_nominalToBinFilter.output();

        if (m_attributeFilter != null) {
            m_attributeFilter.input(tempInst);
            m_attributeFilter.batchFinished();
            tempInst = m_attributeFilter.output();
        }

        if (!m_center) {
            m_standardizeFilter.input(tempInst);
            m_standardizeFilter.batchFinished();
            tempInst = m_standardizeFilter.output();
        } else {
            m_centerFilter.input(tempInst);
            m_centerFilter.batchFinished();
            tempInst = m_centerFilter.output();
        }

        if (m_hasClass) {
            newVals[m_outputNumAtts - 1] = instance.value(instance.classIndex());
        }

        double cumulative = 0;
        for (int i = m_numAttribs - 1; i >= 0; i--) {
            double tempval = 0.0;
            for (int j = 0; j < m_numAttribs; j++) {
                tempval += (m_eigenvectors[j][m_sortedEigens[i]] * tempInst.value(j));
            }
            newVals[m_numAttribs - i - 1] = tempval;
            cumulative += m_eigenvalues[m_sortedEigens[i]];
            if ((cumulative / m_sumOfEigenValues) >= m_coverVariance) {
                break;
            }
        }

        if (!m_transBackToOriginal) {
            if (instance instanceof SparseInstance) {
                return new SparseInstance(instance.weight(), newVals);
            } else {
                return new DenseInstance(instance.weight(), newVals);
            }
        } else {
            if (instance instanceof SparseInstance) {
                return convertInstanceToOriginal(new SparseInstance(instance.weight(), newVals));
            } else {
                return convertInstanceToOriginal(new DenseInstance(instance.weight(), newVals));
            }
        }
    }

    /**
     * Set up the header for the PC->original space dataset
     *
     * @return the output format
     * @throws Exception if something goes wrong
     */
    private Instances setOutputFormatOriginal() throws Exception {
        ArrayList<Attribute> attributes = new ArrayList<Attribute>();

        for (int i = 0; i < m_numAttribs; i++) {
            String att = m_trainInstances.attribute(i).name();
            attributes.add(new Attribute(att));
        }

        if (m_hasClass) {
            attributes.add((Attribute) m_trainHeader.classAttribute().copy());
        }

        Instances outputFormat = new Instances(m_trainHeader.relationName() + "->PC->original space", attributes, 0);

        // set the class to be the last attribute if necessary
        if (m_hasClass) {
            outputFormat.setClassIndex(outputFormat.numAttributes() - 1);
        }

        return outputFormat;
    }

    /**
     * Set the format for the transformed data
     *
     * @return a set of empty Instances (header only) in the new format
     * @throws Exception if the output format can't be set
     */
    private Instances setOutputFormat() throws Exception {
        if (m_eigenvalues == null) {
            return null;
        }

        double cumulative = 0.0;
        ArrayList<Attribute> attributes = new ArrayList<Attribute>();
        for (int i = m_numAttribs - 1; i >= 0; i--) {
            StringBuffer attName = new StringBuffer();
            // build array of coefficients
            double[] coeff_mags = new double[m_numAttribs];
            for (int j = 0; j < m_numAttribs; j++) {
                coeff_mags[j] = -Math.abs(m_eigenvectors[j][m_sortedEigens[i]]);
            }
            int num_attrs = (m_maxAttrsInName > 0) ? Math.min(m_numAttribs, m_maxAttrsInName) : m_numAttribs;
            // this array contains the sorted indices of the coefficients
            int[] coeff_inds;
            if (m_numAttribs > 0) {
                // if m_maxAttrsInName > 0, sort coefficients by decreasing magnitude
                coeff_inds = Utils.sort(coeff_mags);
            } else {
                // if m_maxAttrsInName <= 0, use all coeffs in original order
                coeff_inds = new int[m_numAttribs];
                for (int j = 0; j < m_numAttribs; j++) {
                    coeff_inds[j] = j;
                }
            }
            // build final attName string
            for (int j = 0; j < num_attrs; j++) {
                double coeff_value = m_eigenvectors[coeff_inds[j]][m_sortedEigens[i]];
                if (j > 0 && coeff_value >= 0) {
                    attName.append("+");
                }
                attName.append(Utils.doubleToString(coeff_value, 5, 3) + m_trainInstances.attribute(coeff_inds[j]).name());
            }
            if (num_attrs < m_numAttribs) {
                attName.append("...");
            }

            attributes.add(new Attribute(attName.toString()));
            cumulative += m_eigenvalues[m_sortedEigens[i]];

            if ((cumulative / m_sumOfEigenValues) >= m_coverVariance) {
                break;
            }
        }

        if (m_hasClass) {
            attributes.add((Attribute) m_trainHeader.classAttribute().copy());
        }

        Instances outputFormat = new Instances(m_trainInstances.relationName() + "_principal components", attributes, 0);

        // set the class to be the last attribute if necessary
        if (m_hasClass) {
            outputFormat.setClassIndex(outputFormat.numAttributes() - 1);
        }

        m_outputNumAtts = outputFormat.numAttributes();
        return outputFormat;
    }

    /**
     * Main method for testing this class
     *
     * @param argv should contain the command line arguments to the
     *             evaluator/transformer (see AttributeSelection)
     */
    public static void main(String[] argv) {
        runEvaluator(new PrincipalComponents(), argv);
    }
}
